Product Description
History of Calculus is part of the history of mathematicsfocused on limits, functions, derivatives, integrals, andinfinite series. The subject, known historically asinfinitesimal calculus, constitutes a major part of modernmathematics education. It has two major branches,differential calculus and integral calculus, which arerelated by the fundamental theorem of calculus. Calculus isthe study of change, in the same way that geometry is thestudy of shape and algebra is the study of operations andtheir application to solving equations. A course in calculusis a gateway to other, more advanced courses in mathematicsdevoted to the study of functions and limits, broadly calledmathematical analysis. Calculus has widespread applicationsin science, economics, and engineering and can solve manyproblems for which algebra alone is insufficient. ... Read more

Product Description
In this book, which is both a philosophical and historiographical study, the author investigates the fallibility and the rationality of mathematics by means of rational reconstructions of developments in mathematics. The initial chapters are devoted to a critical discussion of Lakatos' philosophy of mathematics. In the remaining chapters several episodes in the history of mathematics are discussed, such as the appearance of deduction in Greek mathematics and the transition from Eighteenth-Century to Nineteenth-Century analysis. The author aims at developing a notion of mathematical rationality that agrees with the historical facts. A modified version of Lakatos' methodology is proposed. The resulting constructions show that mathematical knowledge is fallible, but that its fallibility is remarkably weak. ... Read more

Customer Reviews (1)

Useless
To the limited extent that this book has to do with Lakatos' philosophy of mathematics it is an unsympathetic and unimaginative summary of some of Lakatos' views interspersed with Koetsier's incompetent extrapolations and misrepresentations.

An example of Koetsier's unreasonable extrapolations is his claim that "Lakatos's views apparently imply that nothing in mathematics is self-evident. Self-evidence in mathematics is an illusion." (p. 24). This statement immediately follows a quotation from Lakatos, Papers, II, p. 42, where Lakatos comes nowhere close to saying anything of the sort.

Another utterly absurd observation is that "Lakatos's notion of 'problem-shift' is similar to Brouwer's notion of 'jump from goal to means'" (p. 64). The latter is a quotation from Brouwer's "Life, Art and Mysticism", which Koetsier quotes as if it was a scholarly work containing "notions" for analysing the development of science when in fact it is a rebellious student manifesto that has nothing at all to do with science or mathematics. The quotation in question in fact occurs in the context of Brouwer's condemnation of modern industrial society.

An example of Koetsier's foolish misrepresentations is his critique of Lakatos' "Cauchy and the Continuum." Here Koetsier misconstrues Lakatos' standpoint by overemphasising the Robinsonian non-standard analysis aspect. Lakatos explicitly concluded that the Robinsonian interpretation is not correct and that its role was that of "a powerful stimulus" (Papers, II, p. 57). Lakatos' argument instead rests ultimately on the claim that Cauchy rejected the canonical counterexample since it diverges at x=1/n (cf. pp. 85-86). Lakatos may very well be wrong, but Koetsier's discussion does not help us decide since it misses Lakatos' point entirely.

The bulk of the book is devoted to Koetsier's proposed improvement on Lakatos: a "methodology of mathematical research traditions" (MMRT). This is amateur philosophy at its worst, complete with ambiguities spewing out its ears and feeble attempts to support it by pretentious terminology that is both ill-defined and never actually used. The latter pillars are often erected on pseudo-Laktosian sand, with pompous distinctions, never employed in the case studies, between e.g. "heuristic progress" (producing conjectures) and "absolute progress" (proving conjectures). It is no wonder that this distinction is never used later, as it is virtually vacuous (no tradition has had only heuristic progress). Koetsier's entire theory in the end amounts to a list of properties that are deemed desirable in a mathematical theory (p. 170), and the dictum that mathematicians should assign a "tradition" a value "proportional to its expected progress", as defined, within a margin of error of fifty-eight thousand miles, by this extremely vague list.

Koetsier's case studies never actually use his MMRT theory in any substantial way (how could they since this theory is all fluff?). One case study is a long and rambling and previously published survey of the history of the theorem on the equality of mixed partial derivatives. Presumably having been forced to include it to meet his page quota, Koetsier is desperately grasping for a way to connect it to his MMRT theory. But this time he does not have the imagination to come up even with fluff. Instead he establishes the desired connection by simply maintaining that the mere existence of research traditions provide resounding proof for his theory: "The different eighteenth century version of the interchangeability theorem ... support the rational reconstruction on the basis of the MMRT ... in the sense that they show the unity of the formalist tradition." (p. 249).

The book is also packed with typos and clumsy formulations. The list on p. 170 referred to above, for example, is said to be "undoubtedly not incomplete", when obviously the opposite is meant. As usual the fat cats at Elsevier want to stick the profits from their ridiculously overpriced books in their own pockets instead of hiring descent proof readers. ... Read more

Product Description
This is a reproduction of a book published before 1923.This book may have occasional imperfections such as missing or blurred pages, poor pictures, errant marks, etc. that were either part of the original artifact, or were introduced by the scanning process.We believe this work is culturally important, and despite the imperfections, have elected to bring it back into print as part of our continuing commitment to the preservation of printed works worldwide.We appreciate your understanding of the imperfections in the preservation process, and hope you enjoy this valuable book. ... Read more

Product Description
This is a reprint of A First Course in Calculus, which has gone through five editions since the early sixties. It covers all the topics traditionally taught in the first-year calculus sequence in a brief and elementary fashion. As sociological and educational conditions have evolved in various ways over the past four decades, it has been found worthwhile to make the original edition available again. The audience consists of those taking the first calculus course, in high school or college. The approach is the one which was successful decades ago, involving clarity, and adjusted to a time when the students' background was not as substantial as it might be. We are now back to those times, so it's time to start over again. There are no epsilon-deltas, but this does not imply that the book is not rigorous. Lang learned this attitude from Emil Artin, around 1950. ... Read more

Customer Reviews (1)

Serge Lang's Short Calculus
This is a reprint of the first edition of what was given its final form by Serge Lang in the 5th edition of his A First Course in Calculus. Both are published by Springer, so it's tempting to make page number comparisons and point out that it takes 500 pages to reach the appendix on epsilon and delta in the 5th edition "First Course" and it takes only 226 pages in the 1st edition "Short Calculus". But the fonts differ, and sometimes Lang broke a paragraph into more than one, and he often added more exercises. Sometimes the extra text is additional examples. He also added graphs and diagrams. The page layout sometimes differs, so occasionally graphs or diagrams take up more space in the 5th edition. It's not the case, then, that the final edition is really twice as long in content as the first.

I have a copy of the 4th edition (Addison Wesley, pub.s) and also a copy of the Short Calculus. As soon as I got this Short Calculus home, I opened the 4th edition and started to compare page-by-page the two books. It's interesting to see what Lang kept and how he revised the chapters from their first edition form. Changes show up already in section 1 of chapter 1, where he adds what amounts to a half-page in the 4th edition within what is page 2 of the 1st edition. But then he's also deleted text from this section: text which amounts to a page and a quarter from the 1st edition version of this section is gone by the 4th edition. Sometimes the changes expand and clarify the text, sometimes they tighten it and make it move quicker. Interestingly, in the section on sums, products, and quotients (Ch 3: The Derivative), he lists the rules at theend of the section of the 1st edition, and in the 4th they aren't there. Chapter 4, on sine and cosine, is significantly expanded from the 1st edition. The appendix on epsilon and delta is also expanded.

From comparing my copy of the 4th edition to what I can see of the 5th through the amazon page-view feature, Lang expanded on the 4th in making the 5th and moving to Springer as his publisher; so the 5th is one more revision removed from the Short Calculus.

Another example of expansion in later editions is the section on rate of change, in chapter 3. In the 1st edition it is a single page long, and in the 4th around 6 pages longer. This is Lang's initial nod to physical applications. This 1st edition has a second appendix following the one on epsilon and delta. In the 4th edition, the content of that second appendix occurs as an introduction to chapter 12, on applications of integration. The appendix is entitled "Physics and Mathematics" and Lang there remarks: "For psychological reasons, it is impossible (for most people) to learn certain mathematical theories without seeing first a geometric or physical interpretation. ... These two [i.e. mathematical theories and the interpretations of them], however, should not be confused." (p. 239) Most calculus textbooks that are currently published mix together the mathematical concepts and scientific applications in which those mathematical concepts are used to model and interpret scientific concepts (or even other mathematical concepts). As Lang points out: "Nevertheless, it is important to keep in mind that the derivative (as the limit of f(x+h)-f(x) / h) and the integral (as a unique number between upper and lower sums), are not to be confused with a slope or an area respectively. It is simply our mind which interprets the mathematical notion in physical or geometric terms. Besides, we frequently assign several such interpretations to the same mathematical notion (viz. the integral being interpreted as an area, or as the work done by a force)." (p. 240)

This book, especially in its 1st edition, is about the mathematics of calculus. It is not a book on "calculus and its applications", as most current calculus textbooks are.

The retail prices for the Short Calculus (paperback) and for the 5th edition of A First Course in Calculus (hardcover) differ by $20 but currently they sell through amazon for essentially equivalent prices. I was fortunate to come across a copy of the Short Calculus at a cost of even less. The advantage of this book is that you can get a first look at calculus in the span of 240 pages. But even Lang's full First Course is shorter than most calculus texts; and the First Course goes beyond the Short Calculus by the addition of four extra chapters, concerned with functions of several variables. Followups to this book (in any edition) are Lang's Calculus of Several Variables, from which the four additional chapters of the First Course are taken (the added chapters are the first chapters of the Calculus of Several Variables), and his Undergraduate Analysis. ... Read more

Product Description
A classic book is back in print! It can be used as a supplement in a Calculus course, or a History of Mathematics course. The first half of Calculus Gems entitles, Brief Lives is a biographical history of mathematics from the earliest times to the late nineteenth century. The author shows that Science and mathematics in particular is something that people do, and not merely a mass of observed data and abstract theory. He demonstrates the profound connections that join mathematics to the history of philosophy and also to the broader intellectual and social history of Western civilization. The second half of the book contains nuggets that Simmons has collected from number theory, geometry, science, etc., which he has used in his mathematics classes. G.H. Hardy once said, A mathematician, like a painter or poet, is a maker of patterns. If his patterns are more permanent than theirs, it is because they are made with ideas. This part of the book contains a wide variety of these patterns, arranged in an order roughly corresponding to the order of the ideas in most calculus courses. Some of the sections even have a few problems. Professor Simmons tells us in the Preface of Calculus Gems: I hold the naïve but logically impeccable view that there are only two kinds of students in our colleges and universities, those who are attracted to mathematics; and those who are not yet attracted, but might be. My intended audience embraces both types. The overall aim of the book is to answer the question, What is mathematics for? and with its inevitable answer, To delight the mind and help us understand the world. ... Read more

Customer Reviews (3)

Some good gems
The "memorable mathematics" part of this book treats many interesting things. One is "a simple approach to E=Mc^2". First we substitute the relativistic notion of mass m=m_0/sqrt(1-v^2/c^2) into F=ma=d/dt(mv) to get the relativistic F=ma, which is F=m_0a/(1-v^2/c^2)^(3/2). The work done by the force moving a particle from 0 to x is energy=integral from 0 to x of relativistic force=(change in mass)c^2.

Another topic is rocket propulsion in outer space. Consider a rocket with no forces acting on it. Then mv is constant since d/dt(mv)=ma=F=0. The rocket moves forward by throwing out parts of its mass in the form of exhaust products with velocity -b relative to the ship. Since mv is constant we have mv at t=mv at t+dt, i.e. mv=(m+dm)(v+dv)+(-dm)(v-b), which reduces to dv=-b(dm/m) which we can integrate to get, e.g. the burnout velocity for given initial conditions b and fuel/m.

But the best topics are two Euler classics. First the summation of the reciprocals of the squares. (sin x)/x has the roots pi, -pi, 2pi, -2pi, ..., which suggests that the "infinite polynomial" (sin x)/x=1-x^2/3!+x^4/5!-x^6/6!+... should factor as (1-x^2/pi^2)(1-x^2/4pi^2)(1-x^2/9pi^2)... Multiplying this out and equating coefficients of x^2 we get 1/pi^2+1/4pi^2+1/9pi^2+...=1/3!, so the sum of the reciprocals of the squares is pi^2/6. Also, as a bonus, if we put x=pi/2 in the infinite product for (sin x)/x we get Wallis's infinite product for pi.

Euler's study of the reciprocals of the squares also led him to the zeta function zeta(s)=1+1/2^s+1/3^s+..., which he saw can also be written as a product: sum over all integers of 1/n^s = product over all primes of 1/(1-1/p^s), as we see by expanding each factor on the right hand side as a geometric series and multiplying out the product, which gives the reciprocal of each possible product of primes, to the power s, exactly once, i.e., by unique prime factorisation, the left hand side. This charming formula immediately pays off by yeilding a new proof of the old theorem that there are infinitely many primes: because zeta(1)=1+1/2+1/3+...=infinity we have also zeta(1) = product over all primes of 1/(1-1/p) = infinity, which is clearly possible only if there are infinitely many primes.

Yes, they are truly gems of exposition
Gems is the correct word to describe the tales in this book. These are some of the best stories of the people who made mathematics what it is today that you will ever find. The first stories are about the ancient Greeks and that amazing flowering of intellectual achievement that suddenly arose on the shores of the Aegean and eastern Mediterranean seas. We will probably never know what events fertilized this amazing garden, but suddenly the purely intellectual pursuits of geometry, number theory and logic became the pinnacle of civilization.
Unfortunately for us all, but an accurate reflection of historical reality, the first set of stories ends at 415 AD and the next does not begin until 1571 AD. However, the pent-up intellectual ferment led to many dramatic changes in a very short time. The germination of calculus could not occur until many philosophical viewpoints were overthrown. Geocentric views of the universe were completely incompatible with the ideas of Kepler and people had to once again believe that the pursuit of knowledge was a worthy task. It was also necessary for the opposition of the established churches to be reduced to a point where at least it was accepted for people to challenge doctrine. This process took over a century, and was not without many conflicts. Two of the greatest minds of the seventeenth century, Blaise Pascal and Isaac Newton, were emotionally unstable and it was manifested in some unusual religious writings.It is conceivable that a longer-lived and more focused Pascal would have invented calculus.
After the second start, the development of calculus then became an inexorable movement. Great intellects followed each other, each building a new section of the castle that is calculus. The author weaves the thread of how each required the achievements of those who preceded them. Personalities and their personal lives also form an integral part of the stories, which makes it much more lively to read. The people who created calculus were real people with sometimes unusual traits. What is striking is that while some were clearly known to be prodigies at an early age, others were quite ordinary in their youth. Newton's youth was quite undistinguished and Weierstrass did not blossomuntil his forties.
This is an ideal book for the study of the history of mathematics. Not only are the facts of development put forward in a sequential order, but you learn about the lives and personalities of the people who made it what it is today. They did not always succeed, were from widely different backgrounds and some of them led very unhappy lives.This should show us all that there is not one specific mathematical personality, but one mathematical discipline that can attract a wide variety of personalities.

A treasure for lovers of advanced math
This is a terrific book for anyone who is fascinated by the workings of great minds.In the first half of the book, Mr Simmons takes us through the lives of 33 of the most notable mathematicians on history, frompre-Archimedes, to the late 19th century.These are wonderful stories ofgreat thinkers, and, to my relief, Mr. Simmons walks us through derivationsof many famous formulas and discoveries.Do not fear that this is allcalculus--much of the book is brilliant algebra, geometry, and numbertheory, and fully comprehendable by anyone with a good non-calculus highschool education.But tasty calculus delights abound for those who are upto the challenge.The second half of the book, called MemorableMathematics, are proofs and insights into some of the most wonderfuldiscoveries of pre-twentieth century Mathematics.Topics include primes,irrational numbers, perfect numbers, proofs of infinite series involving eand pi, and a marvelous treatise on the cycloid and brachistochroneproblems.Interspersed are interesting anecdotes about these greatthinkers, including Newton, Euler, the Bernoulli Brothers, and Leibniz,just to name a few.

I loved this book, even though I am not amathematician by profession.The best part about it is that not only arethese famous formulas presented, but most are also proven, which goes alongway in showing just how amazingly the brilliant minds of these historicalgeniuses work. ... Read more

Product Description
Using the history of mathematics enhances the teaching and learning of mathematics.To date, much of the literature prepared on the topic of integrating mathematics history in undergraduate teaching contains, predominantly, ideas from the 18th century and earlier.This volume focuses on 19th and 20th century mathematics, building on the earlier efforts but emphasizing recent history in the teaching of mathematics, computer science, and related disciplines."From Calculus to Computers"is a resource for undergraduate teachers that provide ideas and materials for immediate adoption in the classroom and proven examples to motivate innovation by the reader.Contributions to this volume are from historians of mathematics and college mathematics instructors with years of experience and expertise in these subjects. Among the topics included are:projects with significant historical content successfully used in a numerical analysis course, a discussion of the role of probability in undergraduate statistics courses, integration of the history of mathematics in undergraduate geometry instruction, to include non-Euclidean geometries, the evolution of mathematics education and teacher preparation over the past two centuries, the use of a seminal paper by Cayley to motivate student learning in an abstract algebra course,the integration of the history of logic and programming into computer science courses,and ideas on how to implement history into any class and how to develop history of mathematics courses. ... Read more

Customer Reviews (2)

Half-baked
This is a careless collection of "notes" most of which were not fit to be printed in this form. Let us consider a few examples.

Hirst tries to tell us about "using the historical development of predator-prey models to teach mathematical modeling." Well, predator-prey systems have the names Lotka-Volterra attached to them, so lets see what they did. If x is the prey population and y the predator population, we have that x'=ax-bxy, where ax represents exponential growth in absence of predators, and -bxy represents deaths, this factor being proportional to xy since this quantity measures the number of "interactions" between predator and pray. This was apparently how Lotka reasoned. Now Hirst tells us: "Volterra appears to have arrived at the interaction terms using somewhat different reasoning, namely a competition argument to suggest that in the presence of predators the prey's effective growth rate should be less than a, and how much less should depend on the predator population" (p. 46). Personally, I doubt that Volterra's reasoning was really "different"; I certainly do not see how one could think of y as acting directly on the growth rate of x without taking xy to measure the number of interactions. In any case, Hirst does nothing to clarify the matter. It seems clear that she herself does not understand the history she is trying to teach, since she is not even sure whether Volterra's reasoning is really different at all. I wonder: how could you possibly justify writing an article professing to be concerned with the history of predator-pray models when you can not even answer this basic question suggested by your own exposition. The fact that Volterra's derivation of the equations "appears" different ought to suggest that anyone with a modicum of self-respect should investigate and clarify the matter before publishing on the subject. But not so in this slapdash book where any half-baked idea goes. Next we learn that "May addressed [the flaw that in the Lotka-Volterra system the predators are always hungry] by replacing the prey death term bxy with a term that approximates bxy for small x an approaches by as the number of prey become large" (p. 48), namely bxy/(x+1). What a nice "approximation" for small x (so for example 9 is "approximated" by 0.9).

Pengelley thinks that we should read "Cayley's 1854 paper 'On the theory of groups, as depending on the symbolic equation Theta^n=1,'" which "inaugurated the abstract idea of group" (p. 3). So Pengelley reprints the paper with added notes. Unfortunately, his notes are very superficial. Mostly Cayley's paper is used as a poor and contrived excuse for discussing standard topics, e.g.: "it is delightfully unclear just how Cayley's initial notion of operation really differs from that of function, and this makes good classroom discussion" (p. 4); or when Cayley happens to mention permutation groups in passing we are told, without further elaboration, that "this is a nice segue to permutation groups for students" (p. 6). As for Cayley's anachronistic definition of groups in terms of "the equation Theta^n=1," Pengelley has no insight to add except for the thoroughly useless recommendation that we should "Note Cayley's interesting point of view here" (p. 5). Again, you would think that if someone decides to write an article on Cayley's paper where the big idea is the equation Theta^n=1 then the author could be expected to have a little more to offer than simply proclaiming that Cayley's idea is "interesting." But, alas, such a proclamation is the only scholarly effort required to warrant publication in this book.

Rogers opts for "putting the differential back into differential calculus." A sensible proposal, and indeed the article starts out promising, with Rogers offering the quick and easy infinitesimal derivation of the derivatives of the sine and cosine. He also tries to offer the infinitesimal proof of the fundamental theorem of calculus, but the exposition is greatly marred by poor figures. Unfortunately Rogers makes a less convincing case when it comes to applications, where he proves trivialities (a circle is the only plane figure with constant non-zero curvature), relies on unexplained physics (catenary), and ends up with problems that his methods cannot solve (brachistochrone). The way to win people over to the classical infinitesimal approach to the calculus is hardly through black-box physics, trivial theorems and unsolvable mathematics.

Valuable information for projects in the history of mathematics
To sit in an upper division classroom and watch a proof unfold, it is easy to be convinced that the creator of the proof was a genius far beyond anything that you can accomplish. When presented to the masses, mathematics is neat, concise and clear. Nowhere in the final product do you see the scribbling down dead ends, the frustration of being unable to see the solution and the early feelings of ignorance. A study of history helps to change all that. A reading of some of the writings of the people who did accomplish great things will show you how they struggled, fought down feelings of inadequacy and persevered until they managed to get it right.
The papers in this collection will help you to understand that even the greats struggled and are grouped into four categories:

*) Algebra, number theory, calculus and dynamical systems.
*) Geometry
*) Discrete mathematics, computer science, numerical methods, logic and statistics
*) History of mathematics and pedagogy

The papers all deal with the history of mathematics and vary from "Introducing Logic via Turing Machines" to "Protractors in the Classroom: An Historical Perspective." I found a great deal of material that can be used in mathematics class. As the two examples cited earlier indicate, some of it is profound and some a little bit quirky. Yet, all of it is important as the use of protractors reflects a major change in how mathematics was taught.
I strongly recommend this book to anyone who teaches the history of mathematics. It can be used as a major reference for student projects or as a source of material for lectures in the history of mathematics that are a bit different from the routine.
... Read more

Product Description
The implicit function theorem is part of the bedrock of mathematical analysis and geometry. Finding its genesis in eighteenth century studies of real analytic functions and mechanics, the implicit and inverse function theorems have now blossomed into powerful tools in the theories of partial differential equations, differential geometry, and geometric analysis. There are many different forms of the implicit function theorem, including (i) the classical formulation for C^k functions, (ii) formulations in other function spaces, (iii) formulations for non-smooth functions, (iv) formulations for functions with degenerate Jacobian. Particularly powerful implicit function theorems, such as the Nash--Moser theorem, have been developed for specific applications (e.g., the imbedding of Riemannian manifolds). All of these topics, and many more, are treated in the present volume. The history of the implicit function theorem is a lively and complex story, and is intimately bound up with the development of fundamental ideas in analysis and geometry. This entire development, together with mathematical examples and proofs, is recounted for the first time here. It is an exciting tale, and it continues to evolve. "The Implicit Function Theorem" is an accessible and thorough treatment of implicit and inverse function theorems and their applications. It will be of interest to mathematicians, graduate/advanced undergraduate students, and to those who apply mathematics. The book unifies disparate ideas that have played an important role in modern mathematics. It serves to document and place in context a substantial body of mathematical ideas. ... Read more

Customer Reviews (1)

could have been a great book
The book is full of typos and mistakes which make every proof a headache to read and understand. This is my third book by the same publisher and they are all of similar quality, full of typos and logical mistakes. Both are deadly sins but they are even deadlier in math books so just stay away from Birkhäuser books when it comes to math. ... Read more

Product Description
This book is a collection of small essays containing the history and the proofs of some important and interesting theorems of analysis and partial differential operators in this century. Most of the results in the book are associated with Swedish mathematicians. Also included are the Tarski-Seidenberg theorem and Wiener's classical results in harmonic analysis and a delightful essay on the impact of distributions in analysis. All mathematical points are fully explained, but some require a certain mature understanding from the reader. This book is a well-written, simple work that offers full mathematical treatment, along with insight and fresh points of view. ... Read more

Product Description
The positive response to the publication of Blanton's English translations of Euler's "Introduction to Analysis of the Infinite" confirmed the relevance of this 240 year old work and encouraged Blanton to translate Euler's "Foundations of Differential Calculus" as well. The current book constitutes just the first 9 out of 27 chapters. The remaining chapters will be published at a later time. With this new translation, Euler's thoughts will not only be more accessible but more widely enjoyed by the mathematical community. ... Read more

Customer Reviews (2)

PART 1 OF BOOK
I was disappointed when I opened the box to find a skinny hardcover 6" by 8" book.I was expecting a full blown thick textbook for the price of $60.This is more of a novelty item for those of you who wish to find out how the theory of differentiation started from scratch.The book has the first steps and analysis that lead to the power rule etc.There is lot of useful information but the notations are a bit a different.This is not a text book with problems and solution.There are examples but these examples are nothing like you'd find in a calculus class.I think this book should be sold for $25 tops.Another thing is that when Euler wrote this book, it had 23 chapters, this is only the first 9 chapters so it leaves you shy of the whole picture.There is about 15 pages on solving Linear Differential equations.I have not read the book word per word yet.So for the intelligent ones, there may be more information they could harvest out of this book.This book is definitely over priced!

A Classic and a Current
While Newton (arguably) founded the subject, Euler (pronounced 'oiler') developed all the methods used today in Differential Calculus.Not only was Leonhard Euler the greatest Mathematician of his day (he actually wroteover a quarter of the tracts from the 18th century!), but he wrote in ahumbling and readable manner such that anyone with a foundation mayapproach his proofs.And this text is no different; simply a book anymathematician should own.Truly one of the milestones of Calculus. ... Read more

Product Description
This comtemporary study of complex dynamics, which has flourished so much in recent years, is based largely upon the work of G. Julia (1918) and P. Fatou (1919-20). The book aims to analyze this work from an historical perspective and show in detail how it grew out of a corpus regarding the iteration of complex analytic functions. This began with investigations by E. Schroeder (1870-71) which he made when he studied Newton's method. In the 1880s, Gabriel Koenigs fashioned this study into a rigorous body of work, and thereby influenced a lot of the subsequent development. But only when Fatou and Julia applied set theory, as well as Paul Montel's theory of normal families, was it possible to develop a global approach to the iteration of rational maps. The book shows how this intriguing piece of modern mathematics became reality. ... Read more

Customer Reviews (1)

Brief Book Review
Alexander's book is a very smart and well-written overview of this particular history-- one not told before at this length and in a book that even those not in the field can generally understand. ... Read more